On a time deformation reducing nonstationary stochastic processes to local stationarity

Marc Genton*, Olivier Perrin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.

Original languageEnglish (US)
Pages (from-to)236-249
Number of pages14
JournalJournal of Applied Probability
Issue number1
StatePublished - Mar 1 2004


  • Exponentially convex
  • Local stationarity
  • Nonstationarity
  • Positive-definite function
  • Reducibility
  • Separable covariance function
  • Stationarity
  • Stochastic processes
  • Time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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